​Heat Pipe Design and Modeling Techniques

This article is based on ACT's Heat Pipe Design and Modeling Techniques and focuses on heat pipe modeling techniques and methods for reference.

A liquid cooling technology exchange group has been established, which is suitable for R&D personnel, product managers, marketers, and other friends engaged in liquid cooling products. 

The following is a video explaining heat pipe technology from ACT, with subtitles added for reference and learning.

A heat pipe is a passive two-phase closed-loop system. Therefore, in any part of the system where there may be thermal conduction limitations—such as insufficient heat dissipation to meet temperature requirements or the need for point-to-point heat transfer—heat pipes can be utilized. For example, transferring heat from an isolated heat source or electronic component to a downstream heat sink in a device is an ideal scenario for heat pipes.

The working principle of a heat pipe is as follows: in the heat input area, known as the evaporator end of the heat pipe, the liquid boils here. Heat is transferred into the system, causing vaporization at this interface and generating steam, which creates a pressure gradient inside the heat pipe. This pressure gradient pushes the fluid toward the cooler areas of the system. As shown in the diagram, heat is pushed from left to right, entering the condenser end, where the latent heat is released, and the steam condenses back into liquid, which is then captured by the wick structure. The wick structure is distributed along the inner diameter of the heat pipe and captures the liquid at the condenser end, creating a passive capillary force that pumps the liquid back to the evaporator end.

Heat pipes have no moving parts, making them highly reliable systems. As long as they operate within their boundary conditions, there are no true failure mechanisms, and they can achieve efficient heat transfer. Due to the presence of latent heat of vaporization, both interfaces exhibit very high heat transfer coefficients, and they can achieve very low temperature gradients, typically between 2 to 5 degrees Celsius.

The advantages of heat pipes are often reflected in size, weight, power, and flexibility. In terms of size and weight, alternative solutions outside of heat pipes often simply increase the volume of the heat sink. While increasing the size of a heat sink can provide some thermal performance benefits, it eventually encounters limitations because heat cannot be further dissipated. Therefore, due to better heat dissipation capabilities, heat pipes can make heat sinks more compact. The greater advantage usually lies in power. In many cases, using a heat sink of the same size, you can increase the heat dissipation power or, through better heat dissipation and improved heat transfer within the system, increase the power while also increasing the size of the heat sink. Ultimately, flexibility is one of the main reasons for choosing heat pipes because they can be bent and arranged in various shapes.

A major issue when using heat pipes is reliability, which is a very real concern. However, this issue can often be mitigated early on because boundary conditions and power requirements will determine whether a heat pipe is suitable. If it can operate within the appropriate conditions for the heat pipe, it should be a long-lasting operating device. Once the system is properly designed and the temperature and power limits are maintained within the range of the heat pipe, it should be a long-lasting design. Such systems have been integrated into very harsh environments, such as defense, aerospace, and medical applications, which have very strict requirements and need long-lasting, highly reliable systems.

The use of heat pipes and the expectations for their thermal performance involve a significant amount of design and modeling work. Two main aspects of improving thermal performance with heat pipes are heat diffusion. For example, in a flat plate, there are three hotspots—two on the top and one on the bottom—where heat cannot be dissipated as quickly as desired to ensure the safe operation of electronic devices. In this case, the flat plate has liquid cooling rails on both sides, and the goal is to conduct heat to these rails and maintain the safe operating temperature of the electronic devices. Although an aluminum plate cannot achieve this due to its thermal conductivity, integrating heat pipes can shorten the path to the liquid cooling rails. In the bottom case, simply adding enough heat pipes to transfer all the power is sufficient. In the top case, the actual heat path is very short, and even with such high heat flux, hotspots still occur. In this case, arranging the heat pipes along the cooling rails to form a long condenser region can also reduce those temperatures.

The heat dissipation power capability of heat pipes has been extensively studied, and there is a wealth of published data on the limits of heat pipes. This is one of the first considerations when using heat pipes for design. There are several limits that restrict the power capacity of heat pipes, including capillary limit, viscous limit, sonic limit, entrainment limit, and boiling limit. For a detailed introduction to the heat transfer limits of heat pipes, please refer to the link below:

Heat Pipe Heat Transfer Limits

In many ground applications, the capillary limit is the primary factor that determines performance. The capillary limit refers to the ability of the wick to pump fluid from the condenser back to the evaporator, and it must overcome all pressure drops in the system. If gravity needs to be overcome for pumping, the largest pressure drop will be the gravitational head. In most applications, devices may be in different orientations or need to operate in different configurations, and they must be able to operate in any type of orientation. Therefore, when faced with this situation, it is necessary to overcome the gravitational head. Another option is to place the condenser above the evaporator if there is flexibility in orientation, and in such cases, a large amount of heat can be transferred. Therefore, these applications primarily operate under the entrainment limit, which is the ability of the steam to overcome the downward flow of liquid shear force and push upward, i.e., the ability to overcome this force. Therefore, in these applications, a large amount of heat can be transferred. The capillary limit is usually the driving factor in ground-type designs, so the limit is a function of several different factors.

The heat transfer limit is mainly constrained by the following factors, which can be used to quickly estimate the capillary limit. The main factors are: (1) Diameter: the larger the diameter, the greater the power that can be transferred. (2) Heat pipe length: the longer the length, the more pressure needs to be overcome. (3) Orientation factors; (4) Fluid properties, mainly determined by the choice of fluid; (5) Wick properties, provided by the supplier.

The bending and flattening guidelines for heat pipes are as follows: the recommended bending radius is three times the outer diameter, which refers to the centerline bending radius. Within this range, performance will not be significantly affected. If the bending radius is smaller, it may limit performance and may cause deformation of the metal shell, potentially leading to potential issues during manufacturing and bending. Therefore, the bending guideline is three times the outer diameter.

For flattening, it is generally recommended to flatten to two-thirds of the outer diameter. At this level, there is still enough steam space to transfer a significant amount of heat. The greater the degree of flattening, the greater the impact on performance. For example, when calculating the capillary limit, the circular diameter is no longer used, and the hydraulic diameter is used for flattened pipes. This limits the steam space and thus limits performance. However, two-thirds is a good guideline that allows the system to transfer a significant amount of heat.

In thermal modeling, different aspects need to be considered, from the enclosure to the heat pipe evaporator. Heat is conducted through welding interfaces, epoxy resin interfaces, or some thermal interface materials, such as gap pads. The heat pipe itself has a temperature difference of 2 to 5°C along its length. Then, from the heat pipe to the heat sink fin structure, heat is usually conducted or transferred through some interface. Finally, there is a temperature rise from the heat sink fins to the air environment. Therefore, to design a system that meets the maximum enclosure temperature requirements, all these factors need to be considered to ensure that the maximum enclosure temperature is not exceeded. Here, the focus is on how to model the heat pipe and the conduction areas around it.

One of the simplest methods to simulate a heat pipe is to use a basic thermal rod. This method can provide quite good results and is highly recommended for a first-order approximation. Essentially, you can try to use a single thermal element to make the system exhibit two-phase performance. The recommended approach is to first input parameters similar to those of a heat pipe into the system, setting an effective thermal conductivity of approximately 10,000 W/mK. The effective thermal conductivity of a heat pipe varies with length, so the shorter the length, the lower the effective thermal conductivity, as the temperature difference is the same over a shorter distance. It is recommended to start with 10,000 W/mK, run the simulation, and then check the temperature difference from the hottest to the coldest point on the heat pipe. Adjust the 10,000 W/mK value until the temperature difference is within the range of 2 to 5°C. If you want to be more conservative, you can set the temperature difference to 5°C. For example, if inputting 10,000 W/mK results in an 8°C temperature difference, continue to increase the effective thermal conductivity until the temperature difference is reduced to 5°C. This is a good approximation of the potential performance of a heat pipe. A 5°C difference is quite conservative, so in many cases, the model can perform better than this, but in practical applications, if you want to be conservative, this is a good first-order method for heat pipe modeling.

HiK Heat Sinks are what ACT calls high thermal conductivity heat sinks. They embed copper heat pipes into aluminum heat sinks and can create HiK heat sinks with various geometric shapes using aluminum surfaces. If you have the processing capability and sufficient area to integrate heat pipes, you can usually make HiK heat sinks. 6061 aluminum, as the heat sink material, has a thermal conductivity of about 167 W/mK. Replacing an aluminum heat sink with a HiK heat sink will significantly improve thermal conductivity, with actual thermal conductivity ranging from 500 to 1200 W/mK in practical applications.

In actual applications, there may be multiple components and multiple heat sinks, and a heat pipe network needs to be designed to achieve the desired or optimal effect. After thermal performance testing, the model is refined to continuously increase the thermal conductivity until it matches the performance test results, usually falling within the range of 500 to 1200 W/mK. This variability or range depends on the operating intensity of the heat pipe, i.e., the length of the heat pipe and the benefits obtained from shorter heat paths.

The most challenging modeling method is the lumped parameter method. In this method, some of the thermal resistances in the steam space are lumped together, and an approximately isothermal steam space is used inside the heat pipe. This provides a good approximation that is closer to reality because it considers thermal interfaces, heat pipe walls, wick structures, and some finer thermal resistances encountered in actual systems. However, it eliminates the need for detailed modeling of two-phase flow and the extremely high heat flux in very small wick structures. This is a method that can provide realistic and accurate predictions while not requiring a lot of computational time to run these models.

The steps for lumped parameter modeling are as follows: First, visit ACT's website and find the heat pipe calculator in the resources section. Then, roughly input your guess for the heat pipe geometry. In this example, take 25 watts of heat and place it in a system to see the geometry. Based on the heat source and heat sink conditions, roughly determine the structure of the heat pipe, with a total length of 3.1 inches, an evaporator length of 1 inch (the heat source area), and a very small condenser, less than 1 inch, resulting in a 1.32-inch adiabatic region. With these input values, you can see the curves on the right side of the diagram, which are the capillary limits for heat pipes of different diameters. The red numbers are the input values required by the calculator, and these curves can be used to accurately determine the operating position and required performance. In this example, the operating temperature range is slightly below 20°C to about 10°C, so it is necessary to run the curve throughout, indicating that a 4 mm heat pipe is needed.

Once the diameter of the heat pipe is roughly determined, you can continue with the lumped parameter model modeling. First, determine the effective thermal conductivity of several paths to conduct heat into the heat pipe, and model each path separately because they are very thin and will slow down the calculation time. Therefore, the total thermal resistance of all these paths needs to be calculated. When calculating thermal resistance, you can see the calculation process here. For example, for solder, you can estimate its thermal resistance based on thickness, the length required to transfer heat through solder, and the effective or actual thermal conductivity of the solder. Similarly, for the copper pipe wall, for a 4 mm pipe, the copper pipe wall thickness is 12 mils, and you can use the thermal conductivity of copper to calculate its thermal resistance. Then, for the wick material, evaporation, and condensation areas, a low thermal resistance is estimated for these areas, and they are lumped together to create a model that can be calculated in a reasonable time to obtain a first-order approximation. It is recommended to model them as 40,000 to avoid creating too thin surfaces, making it easier to model. Essentially, to determine the effective thermal conductivity, all these different areas need to be considered, and then the effective thermal conductivity is determined. Based on these results, the effective thermal conductivity through the interface is 26.7 W/mK, which again shows that heat enters the steam space at the evaporator surface and leaves the steam space at the condenser surface. This is an approximation that can be used as a lumped parameter envelope material, which can consider solder, pipe walls, and wick structures.

The thermal conductivity effect of the steam space is set to a value. Due to the working characteristics of the fluid steam, the steam space is almost isothermal, so the thermal resistance of the steam space is very low. Therefore, the approximation method used here is Fourier's law, which involves power, effective length, area, and temperature difference along the length. Similarly, some values are set for the temperature difference here, assuming a temperature difference of two degrees, which is also a very conservative setting but should provide a good approximation of the thermal conductivity effect. Moreover, this value will be very high because the steam space is almost isothermal.

In summary, heat pipes can be effective components in thermal design and are widely used in many practical scenarios, such as electronic device cooling and aerospace electronics. In fact, there are very few environments where heat pipes cannot operate successfully, but many practical factors need to be considered in each environment.